TTIC 31210: Advanced Natural Language Processing. Kevin Gimpel Spring Lecture 8: Structured PredicCon 2

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1 TTIC 31210: Advanced Natural Language Processing Kevin Gimpel Spring 2019 Lecture 8: Structured PredicCon 2 1

2 Roadmap intro (1 lecture) deep learning for NLP (5 lectures) structured predic+on (4 lectures) introducing/formalizing structured predic+on, categories of structures inference: dynamic programming, greedy algorithms, beam search inference with non- local features learning in structured predic+on generacve models, latent variables, unsupervised learning, variaconal autoencoders (2 lectures) Bayesian methods in NLP (2 lectures) Bayesian nonparametrics in NLP (2 lectures) review & other topics (1 lecture) 2

3 Assignments Assignment 2 due in one week for the report, please use either pdf format or a Jupyter notebook (no plain text) 3

4 <latexit 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/ahtttro7up1z5de7p2svzilvz/5/q/1/+z/t/3//dg+8hogz0n/cf6q/pbtd7pgw//d9gm8z4=</latexit> Modeling, Inference, Learning inference: solve _ modeling: define score funccon learning: choose _ Working defini+on of structured predic+on: size of output space is exponencal in size of input or is unbounded (e.g., machine translacon) (we can t just enumerate all possible outputs) 4

5 What is Structured PredicCon? when we use a structured scoring funccon or structured loss funccon we may be prediccng a structure, but we might not necessarily be building a structured predictor we will use the terms unstructured predictor or local predictor in such cases 5

6 Structured PredicCon a structured score/loss funccon does not decompose across minimal parts of output to apply this definicon we defined parts and minimal parts 6

7 Sequence Labeling (e.g., Part- of- Speech Tagging) determiner verb (past) prep. proper proper poss. adj. noun determiner verb (past) prep. noun noun poss. adj. noun Some quesconed if Tim Cook s first product modal verb det. adjeccve noun prep. proper punc. modal verb det. adjeccve noun prep. noun punc. would be a breakaway hit for Apple. 7

8 parts: determiner verb (past) prep. proper proper poss. adj. noun determiner verb (past) prep. noun noun poss. adj. noun Some quesconed if Tim Cook s first product modal verb det. adjeccve noun prep. proper punc. modal verb det. adjeccve noun prep. noun punc. would be a breakaway hit for Apple. minimal parts: determiner verb (past) prep. proper proper poss. adj. noun determiner verb (past) prep. noun noun poss. adj. noun Some quesconed if Tim Cook s first product modal verb det. adjeccve noun prep. proper punc. modal verb det. adjeccve noun prep. noun punc. would be a breakaway hit for Apple. 8

9 parts: each part is a subcomponent of encre input/output pair parts funccon = decomposicon of input/output pair into a set of parts parts funccons defined for score/loss funccon, rather than for task (many parts funccons possible for a task) parts may overlap minimal parts: smallest possible parts for the task minimal parts funccon defined for task (structured output space), not for structured score/loss funccon minimal parts are non- overlapping 9

10 <latexit 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</latexit> <latexit sha1_base64="cs6ponrgsr2an3paq41qcb5kuru=">aaa77nicxvtzd9w4dlzplngubtp5zasnkhj7lckqt2asjojzrmm7dk67nyqx3ks5dkiiwjc4gqbvvaazn5g3nlzmb+ul/yb3aqwisvdlveq+3skad3fdxcxfoqjkmjbhr//7xy9+7/f/4a9//ocptv/4t/70z/78j1/+xteirhlm38dlvvlviijoxgr6xjkz0e8qtkkezftb6ooztn97tblgzfforip6kzo0ydmwewlv0y9//d97pmiqyt/9kqgil2j772/cnmg5z5u8ah+guzklypxdr2bvpgqebmgzmk72dw8p91ft07anq9ujkpfnyk45dsij50ebrkyszexyho1pwnz7tvkxmkku2/3a4rk9dz+8kirmsjfmnlcxig3ivdn+mcwlfpvjynmocrjvrbbxyeltipjlum6pjfqun6p/os6nixjouu1sytdisck4nyxanundega9onlavhws+bxa3ltnjwpfejqt5brz4rgj7zhkzw9byl+p/7tu0ayzt1p5izrlfegqjhuar+3dfza6e/j9vcobryutzxkotmfgz/lhmss37zbyyfk6l2spuc1iaxucwyymk0ek9bfd/0txb8cbelht2nwekps57bca78x2xs8zxuhekhrzw+qpzcplo43gs0q+dozm+aohxo08mlqdsnqgg0239wlxras0imue8l8zatr3fqc+rydafkbdejgueam1hra3w2hvcrnyf1v9zesjemmezxwaejjdd+cjtqt1mnw2vftze2+vftd47xo8hhmp/7/mosbxd4ln/3ktdrf9h1qqagocg4odb0owf5053fh5twopqyoyvruwohoqiwthjjo4mbqwvb3ym8iamzjtgcxqitvdvgct5zt1ogvhdlhcjy5riawfdyj4nbeh2gw1ke1/dep1xjxtebzsdw30uswqu+jzr0qx9xlfsmxt7pdfqtcbxg45oa+yvegcslvshkvz1hle+fb0jzthh0fqj3a/jt3hzlb3czb98udfhekz1zktpjl4fhjuyysg1gswzxrw8frqisrxjkxn8fmqniqlruufbbahnukwkzn8v8ha1q57ncqxocebitokuw0rfw3ntzz94wumf1vlih+a0azoalkgmmwecenghwwfhytmdgqn4jkb75kq8mwbbcqsqcptliyqjarlgzeq6ri1ksfvnmvlszavm8l4utbr4/kafaksc7n6lgpdupbmlyxxozxialfgvxezydumc0waqeuaszqzt/rn+8ggan7l+dbygkdzye6uavcugydoie4qubmgtfadtxpn4lqqeeatpqhynpt1oo5mllw1xqe3qngp0bam8bzzuag9ksbgr1lawvjm8yew6phfdeheclwfly4zb9edos3siejhyigj7c4jvhmtdk5qos/5ihk+z2gmqlycyijzjqkqwiqmneatlsfzm1l9swezhlw1q4icza/mfxkv0ayo4ytwt5vjoiw2gi5ocq2ifdihmm74xmeaixnbhbfnwdgowcwsmilshrfqakizbxean6eaolq1zrhn22gd6rbgccyz5ujwf3yrxsyka4pwgiykswq5jkjwlrrazy1zu630gnmre6glr6ouv0gf9nxyazfotr0yhibkaopazqjtnoa82jkebwdfnb286kyxoviqcu8qpydvlxxhckcg+cmbxb0eea6jvvvi1gl2ay6oh17djeooop6/ublvk47vb+fiizxtmxenburrl474wyortnx6i7h5q/ik9moonhd6eakud8o3h2tqetcg0i8wr9epltlffdz895dtwbmzcujvvuuyb/ttiezlb6xwqui6kvdrquxq7ujsa5wlwksigyxsfvvpzkswm0hrhtqiknohexjfkcevvyjym2g52/mx7vl4vbupu7fbge524o8gi3uo2v5m9so1fztdqqe+gua7oiuskgk6+gbfvzaoi/yuqvyv1alvnx+axz4ewg4aobahcs1gwvnufvbqum0dir883eoao5lrhazlom4ezlwzvja8ohdbjjd5chpy8ux1ujek02dhzobksljysmckjxjh66lkeqxk5rli4a9t5gxakcbuinqmgu1sr/fhkvgcwd7hd0vcdhjyregjx7qsmnnjdxjvkjkbixqphgdqczmpovt+uv/mzghasket9kphdmj1fsguj4fguzzobtmoxcfrbet9p4rvwsyih+dzcgxnm8hmdbzstrev062mif5kxzkkz0n0qcrhtc3y3dm8kocqcw/3eva61wo+nvaj+bxyvqobybjecnrrlfjhxae7o5pdedd+8fxp67o1a9+tnd0mhegeha2wlrrjvohfd8ro0gupekg1514idu0h3ctmriqedhysagxustzvivc2idcecomy9hiosdhczcq5pe2hjxboy9oj4ntqzfkbtrxvfzxeldybhbzttmyfscjwhab+peddjpwbfrsppwdoxccie091ltchep0/wx5/3qm8gs0yf3iwd8ylahx7eauffy7hvb0uy4c8zbdftai8002dmgc2n9aq3w7ykgjlngqyjk0qe407dtocta4nnheqsn1qlp4rkjcdiec0voim9grxhqbm0ux+eeyg5mozsaqwzoihytvhiozpitubys+aqykpodbal1s8wcimturoqqoalzfnl75msjy77fvhdlblwuyft58nejhkihb8xqc3q486e2d9ck7piscx2b7kxy6djqgdrocmg7njgprifdkm2mwha6f625blfspbogkj9z35abj3wiaqakp0mumc12zdn6x858oordddbrnw20k+dooyhi3cro10vvn/kany33ssb30d6sjkthugzflcbbyz0p3m9yv3ol86m6uipcu0rv3fbvbnmd26pidawlo9ustdvs76kkpmq7xdbma5opponu2sxijzy28gfjna49lxgwhhozwqops8ytgfvo1h3zst1gts89vjjx3iqz4ty1szs5an0wuewsxjaw0w85jls4cdk03svusf3efdc7v2xqpv7gnnt8dvbrmqo41nwnwdj2dhetd3e/8e7idubpy+dvy83p/dhgub4tjz/ayna7ztfa8cd/ccve7mry442rrlxlkok/mxi062adto9sp1mhnro9mresdzp4th8xej89alhp+kpuxfjc9gp3x8qo6a651nbvv7gjzgruelyth/s/kmfhid0/0+uufe2tljhq2/skxbgjibglgkr9tqfowo+gz86qff2jrhwcpgukl0pd+9lguiwzqrhegxqmqhysp/pqfto+8k/lgtibsz3gjapuqk02zdaavb5qmy/l6a25cabawi9ouoqeaawd2wlx0svo657nlovqdpbwhqztyezkm/lu9airfnty6sbeyr/tdspfhuu1pqzui1iarse0nxzhtzmjpisjkphgestq6ru+lwcylxh9widh0hvwepdvgphwbftqs93xgv5kkvawdd7tkj6a0dfg20fztfe3h1jaenyjeqqbymopkiiyd2tzwrjtomuhfvq+uuzohnc8qyiodp0d5gnw+otthcmdjtvtojyrumzjg4yujsyyr5vypdjmpnjgkbyz8qaa8xmrzqjkdq2t9jxlj1z6spoaattqhlz96bxt6as3ib9yvsauzuk6ijlsqcdrseupcrpngctsqbxtyze3iofhibymiiaqndiqddpula6zpzuemyhms27ss88e+fu+z5uc00ybaaaq5keybc9epuver4hkp3g3hr3kpcm0doxtgbiufaifov1u1ertfvldqrehz3r5x4vijq/lu/sdrfmxspmuyvmqunxvqvneouwe0afuxlkg/wwizyfxik6tuxyo+wdydwiksbkbob4/ac4q0twhwv4hfj0huq1ihqgqhtrl30aylrq5y8qicy5vcfdrorfrxjdexcraui3gsrxbjd3ylzj/76ok0ln3hnr6ku4pj4zgylxeqcodhdvkkszcnc9cyjpy9lmjjwuyxfpaq3uslzmhipplv7kvdewrs4x23qao87gnvt70rjkzwgv5drrhjpzt6drplu26ksju/2wj9kz26haxxwtny1e67nqql3r+fbuufz3xj3nmftdxvnab4p44egqtfbgpntbq4yxocxj40xayqtc69v9sc7o3rkmptyr/czarmdr9wday5zzhmn9bsy51a2g0awarpmeipi5qfsewfer8skuzayj45ibio8n0j1j/cikmjf7jy/ph8g3+du8d0tet6ibaeuuyr+e7aor1iyrraliwivigv1aruq00dlqaqrpiiqunwnwbqebxexkmoead96v+re2i1drc9xlxojetjc1jwioe6e88ajbuempx7z7roz3tn5t3wg7w5n0tk9favw8yrsuuv1lnbnymwq+5ctkpm07upzxlnrvshzveou3mu982nobutgzxnymycercye64phxfpgindafiz9i7klfipcb2xuiectwakjlg+osll7hrbq1tqht2fv1mcmthhphjtdryjx1wxjrmjelzgveh4wqoeea1jr3/iguceh2f95zzl8aqcpruxhihmvuydpj90nbtdwulkcik4e9x03ifaoqot4iepnneqq9fm6xww/2/lgzw+fyc70uoujkh0usqrxpzvuyuljytjtm1xnhnbqr5egswlvpcpt+cysy3yncoaxzicfitxwf2zqcnrju0svcgc/op5+bh/lbjowsypoffxdwpkq5bjtzeanl7qptn5pupdtjmb5y43y6pbrme/uzserwl7ow6otnt2bz8qu+6q3tpa6lphq5rtdqfrgtz9ucz3ulhcaj/pfjmtrvnzhkvhrwbntedocwzessvldvszrjkohlifewrlcon4qoqsh6m+qukjfhv4iztsafvacf8skgomig67bgqjnm3z4uxmt63/6qz5kqmfclcss7jomlyhdihz3fyet/1xowc1pp/e2/nd48rm3hl4te3lrvlxbw5iwgzosydrcdp8ucad/kwi1ukxznc48zmkkd/f9a22sker93cbikovaotdp1pojjd2rhzlaymrjauetv40xyqoeqsvcymz4sbflzyuhp4ms7ixval7dlo+docbthanfvmg+yagxcb39gt3lyzuxl5rdubma5x6nrkxz0fvzwj2i0cumq4cs/vidpnrdb2rwu5q3ermghag2wlmpnrwo2z/h2cpu2lfsqo7paqwt9gsywt9wolfk2npfzpm6r8pgluaxnbrxpvavrrg/ya6em5l28hwfnizvsjrs5a0uivcc4m9wwy+ftnbeqnbtkwbvb5tldcrynjynygruw9tdp2pnsj6kxd1evpgjwpzswsrxkqsqnetw5/vdfzrkqiic4jo33e+2edd9nauq3tfcglckl1up1jlwnnevf83zonaaxyuvwdv5agb+tqkzobnfa6ce9lqvdqgm4fxqghmjkwxqv+yogm/7ym3fup2s6f6ypm263zfbmbh2v/gpzib2n8i4h988ozwchu7+7e93fv3p3z/ppnj6q62/3nq4ndn6h61fb73aott6vxu/oh5ahlw+udqujv/j+d+p/0tdf/rf1+cvt4yf4//+p9hqupo=</latexit> Parts and Score FuncCons given a parts funccon our score funccon is then defined: score funccon decomposes addicvely across parts each part is a subcomponent of input/output pair 10

11 <latexit 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k05arr79umggex5pcboejf1hfloz+oan5gxhmzik1khwm+ghhtjvzpxsoutia7iviv6mw+qngjmim62x7b7oxn57gmzgxgg4nyburtr1nx1lvajtngshlvcyxz8xlia0ms7ufnka5lcquieg6200m9a9oxp8wxln+hbdjxhexzbc/sshvc3ju6savz0ev2/zlgq0awnwehzyx6rsxuxv0kvn3ca9pbvhzkml2msspgllolqgudpccovhk1wxkjw0ysgm2+bc33k2dyicwfqhsdupthux5astor+ikwxx4d5uyojlxmivcvi0u8puv9mlivqbme1a7rfbfo6+zixtl+jurjbslguhdrlwnvevv40z4paetwqraheluob+pg6bgrngv479baxujycybiulgeyl6ziborx3ahwsv+57ru3nztdx9a0tff7ohggw+43/thmxp4tgffjq/thk+ojye/+cefx/9t9+cwptv rcmw7/y+vxw862zrtdb0z33d/7tzr/f+y8h//ngvx7894p/mddvfdbr/nxw6ofb//0/vhkhjq==</latexit> Structured PredicCon Tasks task output structure minimal parts mulc- label classificacon set of N labels, each of which can be true or false set containing individual labels in label set

12 <latexit sha1_base64="yz3htpnwmceleyr2zdoyxl9yqka=">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</latexit> <latexit sha1_base64="cs2rlstvqqvviaakpmv2nv3uyg0=">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 rcmw7/y+vxw862zrtdb0z33d/7tzr/f+y8h//ngvx7894p/mddvfdbr/nxw6ofb//0/vhkhjq==</latexit> Structured PredicCon Tasks task output structure minimal parts mulc- label classificacon set of N labels, each of which can be true or false set containing individual labels in label set sequence labeling label sequence with same length T as input sequence; each label is one of N possibilices set containing labels at posicons in output sequence

13 <latexit sha1_base64="jsds54fqdxzur0kyw95axmi6x5y=">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</latexit> <latexit sha1_base64="jwvgxgsfqlmoeat2y/eexn5cudg=">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</latexit> <latexit sha1_base64="ftgq3472u45v49/gf2nlk1ywjqm=">aaacwnicbzflswmxemezq/bpoz5uxokl0kkwxrh0ofdw4rgcrujblmyabuozd5nzbvn2s3orwa8imd4e2zoq+m9vzsjkhzcsxiflfrrmxuzwjpvlf4rbo7t7pf2dtgpjsvmlhikuzy5rtpcatycdym+rzmr3bxtyr3ft+tmrk4qhwsnmitbzysdghqcenhjkl5wut2doesk4dqdf4lnkidenafu3yb6bvt+cbm7tthagvzcsowrodwetsithgqc1p1s26tys8lqwf6kmftf0su/dfkhjnwvabvgqy1sr9biigvpb0ki3viwideqgrknlqhymesnmmhrxnoljl5t6bibn9o9eqnyljno7xjmuqlzru/hfrrodd91lebdfwai6v8ilbyyqt33gfs4zbthrgldj9a6ydokkfprvflqj9uqt10x7om5bdfvhsty4wdirq8fobfwrja5qa92jjmohij7qt5exssaxazp5szhvny3fzcfacvpobzmjtrk=</latexit> <latexit sha1_base64="a38qrsspdnywx+ag7+vp/plcoks=">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</latexit> <latexit sha1_base64="s1iwp5sygdviyw8yj8erkmsp2nc=">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</latexit> <latexit sha1_base64="9ioh81oa2m85rl/x9t/omzcmtac=">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</latexit> Feed- Forward POS Tagger what is the parts funccon for this model & loss? 13

14 <latexit sha1_base64="jsds54fqdxzur0kyw95axmi6x5y=">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</latexit> <latexit sha1_base64="jwvgxgsfqlmoeat2y/eexn5cudg=">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</latexit> <latexit sha1_base64="ftgq3472u45v49/gf2nlk1ywjqm=">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</latexit> <latexit sha1_base64="a38qrsspdnywx+ag7+vp/plcoks=">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</latexit> <latexit sha1_base64="s1iwp5sygdviyw8yj8erkmsp2nc=">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</latexit> <latexit sha1_base64="9ioh81oa2m85rl/x9t/omzcmtac=">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</latexit> Feed- Forward POS Tagger what is the parts funccon for this model & loss? is this a structured predictor? no. parts funccons decomposes like the minimal parts (in terms of y) 14

15 <latexit sha1_base64="jsds54fqdxzur0kyw95axmi6x5y=">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</latexit> <latexit 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Forward RNN for Part- of- Speech Tagging if the car hidden vector used to compute probability distribucon over tags at each posicon: IN DT NN

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Forward RNN for Part- of- Speech Tagging if the car IN DT NN loss:

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Forward RNN for Part- of- Speech Tagging if the car what is the parts IN funccon for DT this model NN & loss? is this a structured predictor? no

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Forward RNN for Part- of- Speech Tagging with Previous Label if the car IN DT NN this model uses the previous y to compute a hidden vector

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Forward RNN for Part- of- Speech Tagging with Previous Label if the car IN DT NN hidden vector used to compute probability distribucon over tags at each posicon:

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Forward RNN for Part- of- Speech Tagging with Previous Label if the car IN DT NN loss:

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Forward RNN for Part- of- Speech Tagging with Previous Label if the car IN DT NN what is the parts funccon for this model & loss?

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Forward RNN for Part- of- Speech Tagging with Previous Label if the car is this a structured predictor? yes. parts funccons does not decompose like minimal parts (in terms of y) IN DT NN

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rcmw7/y+vxw862zrtdb0z33d/7tzr/f+y8h//ngvx7894p/mddvfdbr/nxw6ofb//0/vhkhjq==</latexit> Structured PredicCon Tasks task output structure minimal parts mulc- label classificacon set of N labels, each of which can be true or false set containing individual labels in label set sequence labeling label sequence with same length T as input sequence; each label is one of N possibilices set containing labels at posicons in output sequence

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rcmw7/y+vxw862zrtdb0z33d/7tzr/f+y8h//ngvx7894p/mddvfdbr/nxw6ofb//0/vhkhjq==</latexit> Structured PredicCon Tasks task output structure minimal parts mulc- label classificacon set of N labels, each of which can be true or false set containing individual labels in label set sequence labeling label sequence with same length T as input sequence; each label is one of N possibilices set containing labels at posicons in output sequence labeled segmentacon

25 Named EnCty RecogniCon Some quesconed if Tim Cook s first product would be a breakaway hit for Apple. PERSON ORGANIZATION 25

26 Labeled SegmentaCon as Sequence Labeling O O O B- PERSON I- PERSON O O O Some quesconed if Tim Cook s first product O O O O O O B- ORGANIZATION O would be a breakaway hit for Apple. B = begin I = inside O = outside 26

27 <latexit sha1_base64="yz3htpnwmceleyr2zdoyxl9yqka=">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</latexit> <latexit 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rcmw7/y+vxw862zrtdb0z33d/7tzr/f+y8h//ngvx7894p/mddvfdbr/nxw6ofb//0/vhkhjq==</latexit> Structured PredicCon Tasks task output structure minimal parts mulc- label classificacon set of N labels, each of which can be true or false set containing individual labels in label set sequence labeling label sequence with same length T as input sequence; each label is one of N possibilices set containing labels at posicons in output sequence labeled segmentacon

28 <latexit sha1_base64="yz3htpnwmceleyr2zdoyxl9yqka=">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</latexit> <latexit 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rcmw7/y+vxw862zrtdb0z33d/7tzr/f+y8h//ngvx7894p/mddvfdbr/nxw6ofb//0/vhkhjq==</latexit> Structured PredicCon Tasks task output structure minimal parts mulc- label classificacon set of N labels, each of which can be true or false set containing individual labels in label set sequence labeling label sequence with same length T as input sequence; each label is one of N possibilices set containing labels at posicons in output sequence labeled segmentacon unlabeled dependency parsing

29 Dependency Trees a dependency is a relacon between a word (a head or parent) and its dependent (its modifier or child) a dependency tree for a sentence contains a dependency for each word in the sentence drawn as a directed tree with parents poincng to children one word is the root of the tree

30 Labeled Dependency Trees more common to use labeled dependency trees where each dependency has an associated label: DET = determiner NSUBJPASS = nominal subject in passive construccon AUXPASS = auxiliary verb in passive construccon TMOD = temporal modifier PUNCT = punctuacon

31 a longer sentence: rearranging the words a bit, we now have a non- projec+ve dependency tree (i.e., tree with crossing dependencies):

32 Dependency Parsing dependency parsing is the task of prediccng a dependency tree for a sentence one of the most widely- studied structured prediccon problems in NLP used for several downstream NLP tasks 32

33 ApplicaCons of Dependency Parsing widely used for NLP tasks because: faster than consctuent parsing captures more semancc informacon text classificacon (features on dependencies) syntax- based machine translacon relacon extraccon e.g., extract relacon between Sam Smith and AITech: Sam Smith was named new CEO of AITech. use dependency path between Sam Smith and AITech: Smith à named, named ß CEO, CEO ß of, of ß AITech 33

34 <latexit sha1_base64="hhsevwvbrpxzaew00e9ejadzqzi=">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</latexit> minimal parts for (unlabeled) dependency parsing: each y t holds the index in the sentence x of the parent of word x t we use 0 for the ROOT anachment 34

35 Unstructured Predictors for Dependency Parsing how might you design an unstructured predictor for dependency parsing? build a predictor that predicts the index of the head for a word can use full sentencal context, just can t score mulcple dependencies in any single scoring term fast, simple, works ok, but doesn t guarantee a tree structure (may have cycles, etc.) 35

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k05arr79umggex5pcboejf1hfloz+oan5gxhmzik1khwm+ghhtjvzpxsoutia7iviv6mw+qngjmim62x7b7oxn57gmzgxgg4nyburtr1nx1lvajtngshlvcyxz8xlia0ms7ufnka5lcquieg6200m9a9oxp8wxln+hbdjxhexzbc/sshvc3ju6savz0ev2/zlgq0awnwehzyx6rsxuxv0kvn3ca9pbvhzkml2msspgllolqgudpccovhk1wxkjw0ysgm2+bc33k2dyicwfqhsdupthux5astor+ikwxx4d5uyojlxmivcvi0u8puv9mlivqbme1a7rfbfo6+zixtl+jurjbslguhdrlwnvevv40z4paetwqraheluob+pg6bgrngv479baxujycybiulgeyl6ziborx3ahwsv+57ru3nztdx9a0tff7ohggw+43/thmxp4tgffjq/thk+ojye/+cefx/9t9+cwptv rcmw7/y+vxw862zrtdb0z33d/7tzr/f+y8h//ngvx7894p/mddvfdbr/nxw6ofb//0/vhkhjq==</latexit> Structured PredicCon Tasks task output structure minimal parts mulc- label classificacon set of N labels, each of which can be true or false set containing individual labels in label set sequence labeling label sequence with same length T as input sequence; each label is one of N possibilices set containing labels at posicons in output sequence labeled segmentacon unlabeled dependency parsing tree over the words in the input sentence; each word has exactly one parent set containing indices of parent words for each word in sentence condiconal generacon sentence (or a paragraph, document, etc.)

38 <latexit sha1_base64="f6upsv2ea2kjoks95b91mesmeuy=">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</latexit> CondiConal GeneraCon for machine translacon and other condiconal generacon tasks, input is a sequence and output is a sequence minimal parts for these tasks: each y t is a word from the output vocabulary 38

39 Unstructured Predictors for Machine TranslaCon how might you design an unstructured predictor for machine translacon? assume a max length of the translacon, pad to that length, build predictors that predict the word in posicon t in the translacon this probably won t work very well, but if we have this model we could maximally parallelize translacon across machines 39

40 <latexit 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Sequence- to- Sequence Models with AnenCon most common approach for condiconal generacon previously- predicted output symbol used as input for making next prediccon ( auto- regressive ) is this a structured predictor? yes

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rcmw7/y+vxw862zrtdb0z33d/7tzr/f+y8h//ngvx7894p/mddvfdbr/nxw6ofb//0/vhkhjq==</latexit> Structured PredicCon Tasks task output structure minimal parts mulc- label classificacon set of N labels, each of which can be true or false set containing individual labels in label set sequence labeling label sequence with same length T as input sequence; each label is one of N possibilices set containing labels at posicons in output sequence labeled segmentacon unlabeled dependency parsing tree over the words in the input sentence; each word has exactly one parent set containing indices of parent words for each word in sentence condiconal generacon sentence (or a paragraph, document, etc.) set containing each word in the output

42 Other Tasks? some tasks do not permit an easy definicon of minimal parts 42

43 ConsCtuency Parsing (S (NP the man) (VP walked (PP to (NP the park)))) S VP NP PP NP DT NN VBD IN DT NN the man walked to the park Key: S = sentence NP = noun phrase VP = verb phrase PP = preposiconal phrase DT = determiner NN = noun VBD = verb (past tense) IN = preposicon 43

44 SemanCc Role Labeling ARG0 = usually agent ARG1 = typically pa=ent or theme ARG2 = open beneficiary

45 Other Tasks? some tasks do not permit an easy definicon of minimal parts consctuency parsing, semancc role labeling, etc. somecmes we can cast these as condiconal generacon tasks, then inherit the minimal parts definicon from condiconal generacon 45

46 <latexit 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Sequence- to- Sequence Models with AnenCon input and output sequences can have different lengths we can frame many output structures as sequences

47 FormulaCng ConsCtuency Parsing as CondiConal GeneraCon {Vinyals, Kaiser} et al. (2015): Grammar as a Foreign Language

48 FormulaCng ConsCtuency Parsing as CondiConal GeneraCon {Vinyals, Kaiser} et al. (2015): Grammar as a Foreign Language

49 others have done this for dependency parsing, semancc role labeling, abstract meaning representacon parsing, and many other tasks sequence- to- sequence models then become a general purpose modeling framework for many structured prediccon tasks 49

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Modeling, Inference, Learning inference: solve _ modeling: define score funccon learning: choose _ 50

51 <latexit 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hwqhfefztqvldvyfnx6mg6h3nwq9w8lzihvrs6tom8qw67tt24ghoc7b2vuiah67qetce4rvtcztu5r4ek3b+2ce81ru9ulvmdocp2sp117y9wzv/kfnxze+rybgmm9/4rzmj809k7i8v7u2o9nzhf39/45m/n38+8+bab9b+shz7bbt2p7vp1p6sha89xwtv/fpwv2/959z/3//f/v/f/+3932nog7caml+t9x7uv/n/igns0g==</latexit> Inference with Structured Predictors inference: solve _ how do we efficiently search over the space of all structured outputs? this space may have size exponencal in the size of the input, or be unbounded complexity of inference depends on parts funccon 51

52 Hidden Markov Models simple, useful, well- known model for sequence labeling: Hidden Markov Model (HMM) HMMs are used in NLP, speech processing, computaconal biology, and other areas 52

53 <latexit 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Hidden Markov Models n- gram language models define a probability distribucon over word sequences x HMMs define a joint probability distribucon over input sequences x and output sequences y condiconal independence assumpcons ( Markov assumpcon ) are used to factorize this joint distribucon into small terms *for now, we are omiwng stopping probabilices for clarity 53

54 <latexit sha1_base64="eo7jwtraydl/2gavxyynwrsnlhw=">aaaefniclvnbb9mwfpbaacpconjkxvavfbqfjc2svjo0irckxgzia1htrbbjtnacixihqcjl/ah+gw/8fl5w0nu3cbbk+zzzfcff8bgny85syzq/dipv7cbnw7u39tt3791/unt7ejzgwulokyl4lawwsilnit0vtha6ibokasxph1+8lfd+f5qklao/iwlmrweah8xnbakvcvcqpxohj61ubxieempgcv2zmg0nqglcre4dljslx6ecy+fxgchgivii2m8n0rxgebyszlazrza8jsobo5z6ormi9qwd6zifovabhh2tci1vo86624yodb0ls7xeshqsnp6ile3/vlm21tr/ooyj7qxtqc252uwirgoo3afpqg32nx3dmmovmsab0pg79jz6ui62z9e1+pxo3bfrvjl5kh0wzhycf5tn3goium+q8q62uqbyibcjucrvza2ej2el4uxrigsvbvmafk9l9wyvfgn/hwox3lyn3vrdnmxywmugntfqyd5o3nppx4tiftbqei7sdgizsrjl6kkywqnunsylmsixaeyhygxrqnnrxn4fcrsq4ke/stqmbsyj6xk5ctli8hszqdxdxorgvdgwe353llmwzgqnyuzizzguesz+ivryqongu2ugkjbvkyqtlcai1i/vvros7snfns5swzin60onfvz++6wdu+axeaqawakh4bi8ayfgfjdk7+qt6otqswpam+1aezmjvnbmlxwenobw/qozg3di</latexit> <latexit sha1_base64="3ud9r9hdqd5cwnidvodo8jsplgk=">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</latexit> <latexit sha1_base64="lxldkeoexjrosojqjmku8lffojo=">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</latexit> Random Variables for Sequence Labeling let s define random variables for observacons: observacon variable at Cme step t: its possible values: words in vocabulary and we ll define one hidden variable for each observacon: hidden variable at Cme t: its possible values: discrete symbols in some set for now, think of the set of possible POS tags 54

55 <latexit 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sha1_base64="tfb9hqoyojdollwkxkrkxxl2r+y=">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</latexit> CondiConal Independence AssumpCons of HMMs two Y s are condiconally independent given the Y s between them: an X at posicon t is condiconally independent of other Y s given the Y at posicon t: *for now, we are omiwng stopping probabilices for clarity 55

56 <latexit sha1_base64="wz++3edxjznks+4krtl2ja/x4ni=">aaa2xxicvvtbc924kdamk82sspez7oo+mjgutwjj0xe2tmqmxdua27ft49f6fzmbkktaeochfm8gwhmxzewpyi/kv0k3whnixcjjevhv2skarxunrnejcvfuzuzi4+o/fftxrz/89j9+9sk/b//8x/713/ 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HMMs condiconal independence assumpcons à we only have to worry about local distribu+ons: transi+on parameters: emission parameters: *for now, we are omiwng stopping probabilices for clarity 56

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